# Target Test Prep EA Quant Challenge Problem 3

### Challenge Question

Last Sunday, the Stewart Vineyard ran a price promotion in which it sold red wine for r dollars per case and white wine for w dollars per case. What was the ratio of the revenue from red wine to the revenue from white wine?

1) Last Sunday, the Stewart Vineyard sold each case of red wine for 3 times as much as each case of white wine.

2) Last Sunday, the Stewart Vineyard sold 2 times as many cases of white wine as it sold of red wine.

**Solution:**

__Question Stem Analysis:__

If we let x = the number of cases of red wine sold, the revenue from red wine can be expressed as rx. Similarly, if we let y = the number of cases of white wine sold, the revenue from white wine can be expressed as wy. Thus, the ratio we're looking for is

Remember that we'll need to produce a constant ratio in order to produce a meaningful ratio.

__Statement One Alone:__

This means that r = 3w, which we can substitute for r in our ratio:

This is not sufficient because there are still two different variables in the fraction. Different values of x and y would change the value of the fraction. Statement one alone is not sufficient.

Eliminate answer choices A and D.

__Statement Two Alone__**: **

This means that y = 2x, which we can substitute for y in our ratio:

This ratio is not sufficient because there are two different variables in the fraction. Different values of r and w would change the value of the fraction. Statement two alone is not sufficient.

Eliminate answer choice B.

__Statements One and Two Together:__

Substituting the information from both statements for variables in our original ratio, we can produce the following fraction:

Thus, the ratio of revenue from red wine to revenue from white wine is 3:2. Statements one and two together are sufficient to answer the question.